Measuring devices of this type are generally known, and are used within the scope of dimensional production measurement technology, in particular for measuring cylinder bores in internal combustion engines for motor vehicles. The known measuring devices have a base body for supporting on the workpiece, and a measuring head which has at least one sensor for scanning the inner wall of the cavity. The known measuring devices also have a shaft that is connected to the base body, the measuring head being movable relative to the base body in the axial direction of the shaft and rotatable about a rotational axis defined by the shaft in the known measuring devices, the shaft is used as a guide shaft, along which the measuring head moves in the axial direction in order to be able to approach different axial locations on the inner wall in the axial direction of the cylinder bore, and about which the measuring head rotates in order to scan the inner wall of the cylinder bore in its peripheral direction.